Comcast Corp.
is taking on the Murdochs. The question is how far it wants to go.

The cable giant on Wednesday lobbed an official $31 billion proposal to buy European pay-TV operator Sky PLC, topping an existing offer from
21st Century Fox Inc.,
which already owns a 39% stake in Sky. Fox counts Rupert Murdoch and his family as major shareholders.

The official Comcast offer sent Sky shares nearly 4% higher—and above the Comcast bid, suggesting investors are positioning for a bidding war. 21st Century Fox said it remains committed to buying all of Sky.

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Separately, Comcast is weighing whether to play interloper on Fox’s $52.4 billion deal to sell its entertainment assets to
Walt Disney Co.
, people familiar with the situation say. Comcast is gaming out the possibility of making a public case to Fox’s shareholders that they should reject the Disney deal, which is expected to come to a vote this summer, and opt for a Comcast tie-up instead, people familiar with the situation said.

Comcast lost out to Disney in December when Fox rejected its bid, which was 16% higher, according to a Fox regulatory filing last week. Fox cited concerns about regulatory risk. The assets in play include Fox’s film and TV studio, cable networks and international properties including Star India and the Sky stake.

Comcast may choose to leave the Disney-Fox deal alone, and it doesn’t expect to make a decision in the near term, the people familiar with the situation said.

A major consideration for Comcast to pursue any further deals is its languishing stock price. As of Wednesday’s close, Comcast shares had declined 20% since late January, wiping out more than $39 billion in market value.

Comcast Chief Financial Officer Michael Cavanagh said on the quarterly earnings call that the company was unlikely to use its stock to make deals when the price is at these levels. He said the company’s strong balance sheet will give it flexibility to consider opportunities “at times like this.”

If Comcast chooses to go hostile for the Fox assets, Comcast would need to woo Fox investors, which may not be easy. Comcast has had conversations with several shareholders in the wake of its Sky bid, including British investor TCI Fund Management, known for its activism, people familiar with the situation said.

In recent weeks, TCI founder Chris Hohn spoke on the phone with Comcast Chief Executive Brian Roberts and probed about Comcast’s interest in launching a public bid for Fox’s assets, people familiar with the situation said. Mr. Roberts didn’t respond, the people said. Other TCI officials have also had conversations with Comcast’s investor relations team that left Comcast executives with the clear indication that TCI wants the cable giant to continue its pursuit of Fox, the people said.

In an email this week, Mr. Hohn said he didn’t urge Mr. Roberts to go hostile in pursuit of Fox’s assets.

Mr. Murdoch and his family have a 39% voting interest in Fox. Their economic interest, which is what would count in a shareholder vote on the Disney-Fox merger, is roughly 17%. The Murdoch family is also a major shareholder in
News Corp,
the parent company of The Wall Street Journal.

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Comcast is offering £12.50 ($17.47) a share for Sky, or 16% more than Fox’s £10.75-a-share bid. On the earnings, call, Comcast executives assured investors that it would be a sound investment, highlighting Sky’s broadband service and original programming arm to emphasize it is much more than a satellite TV provider.

Mr. Roberts on Wednesday that Comcast loved its core businesses, adding: “anybody who is viewing this as some diversion from that is not reading us properly.”

British regulators have held up Fox’s takeover bid as they examine whether it would give Mr. Murdoch and his family too much influence in U.K. media. News Corp publishes three major British newspapers.

Regulators are expected to deliver a final recommendation on Fox’s proposal on May 1, and then the British government will decide whether to approve the merger outright, approve it with conditions, or reject it.

For the quarter, Comcast’s growth was powered by its NBCUniversal media unit, where revenue rose 21% to $9.5 billion. Comcast lost 96,000 cable TV customers, compared with a gain of 42,000 in the prior-year quarter.

Quarterly profit rose 21% to $3.1 billion, or 66 cents a share, up from $2.6 billion, or 53 cents a share, a year ago.